As the crisis deepens between Mayor de Blasio and the cops, I’m prompted to wonder what Calvin Coolidge would do.

The 30th president rose to national prominence by facing down a strike by the cops in the hometown of our own police commissioner, Bill Bratton. Is there a role here for Gov. Cuomo?

Back in 1919, Coolidge was governor of Massachusetts. When police in Boston walked off the job, he backed the Boston police commissioner’s refusal to negotiate.

He reckoned that officers sworn to protect the public safety just don’t have a right to strike.

News that arrests and other law-enforcement activity in New York are suddenly plummeting this week is a Coolidge moment. The development, first reported in Monday’s Post, suggests that cops aren’t just turning their backs on the mayor.

The Post’s scoop suggests that a significant number of cops are purposely hanging back in the wake of the assassination of Officers Rafael Ramos and Wenjian Liu. Overall arrests are down 66 percent. Officers are not policing as aggressively as they normally do.

That means we’re facing what The Post calls a “virtual work stoppage” — a slow-motion strike.

This may on the surface seem understandable. If the mayor isn’t going to back up New York’s Finest, the rank and file can be expected to try to minimize the risks they take.

Even if it’s understandable, though, it’s unacceptable.

It’s perilously close to the kind of strike action that Coolidge calculated couldn’t be countenanced. Not in Boston. Not in New York.

The Boston police strike took place amid growing de Blasio-type Bolshevism in cities. A general strike in Seattle had been followed that year by an assassination attempt on its mayor — who then quit, announcing he was exhausted and planned to go fishing.

In Boston the cops had serious grievances. They were paid but $1,400 a year, recruits even less. They had to buy their own uniforms, which took up a seventh or more of their salaries. They’d been pulling extra duties during the war — and had received no raises to make up for postwar inflation.

The commissioner had suspended 19 of their number for serving in a union that he’d ordered the force not to found.

When the Boston police struck, it was no “virtual” slowdown. The cops literally walked out of the station houses, carrying their helmets under their arms. More than 70 percent of the force went out. Soon shops were being looted, people were endangered.

In the North End, ruffians terrorized girls. Rapes were reported. “For the first time in the memory of man, Boston was given over to lawlessness,” is how The Boston Globe put it in an extra edition for the strike.

When the head of the American Federation of Labor, Samuel Gompers, urged striking cops to return, Police Commissioner Edwin Curtis refused to take them back. Coolidge backed him up, calling out the entire State Guard — which kept the public safe until new officers were hired.

Coolidge also sent Gompers a telegram that ended with the famous words (using cable lingo): “THERE IS NO RIGHT TO STRIKE AGAINST THE PUBLIC SAFETY BY ANYBODY COMMA ANYWHERE COMMA ANY TIME STOP.”

Could Mayor de Blasio summon this kind of principle? It would be inaccurate to suggest the situation in New York is the same as Boston in 1919. But even a “virtual” work stoppage by police is far different from a silent protest. It is a serious matter.

De Blasio is in a worse bind than Coolidge was. By failing to back the police when they were under attack in the courts and the press and by protesters, he has impaired his moral authority over the men in blue.

Coolidge hadn’t made that blunder. He was governor, who, in those days, named the Boston commissioner. Yet Coolidge acted only after the situation reached a crisis, creatively using the State Guard to restore order.

Could this happen in New York? Could Andrew Cuomo step in to assert his authority as governor?

Could he back the police in all the court challenges and the protests while making it clear he’ll get tough on any work stoppage, “virtual” or otherwise?

Well, I’m not a lawyer — but good lawyers can surely help the governor find some pretext for intervening.

The question intrigues. All the more so because of the outcome for Gov. Coolidge after he made his stand on principle in the Boston police strike.

The Republican Party promptly put him up for vice president on Warren Harding’s ticket. By the end of 1920, he was the vice-president-elect. In 1923, he succeeded to the presidency — a reminder that police strikes can have consequences.